Optical frequency comb (OFC) generators play crucial roles in various applications, including optical communications [1–3], spectroscopy [4,5], timekeeping [6], precise ranging [7,8], and exoplanet detections [9], by providing excellent light sources with coherent and equally spaced spectral lines. Recent progress in photonic integrated circuits has paved the way for on-chip comb sources, with significantly improved compactness, efficiency, and scalability [10–14]. Integrated OFCs have been achieved based on various physical principles and material platforms, including mode-locked semiconductor lasers (e.g., in GaAs [15] and InAs [16]), optical Kerr nonlinearity (e.g., in SiN [17–19], AlN [20], and AlGaAs [21]), and electro-optic (EO) modulation (e.g., in LN [22–26] and Si [27]).

Among these schemes, electro-optic frequency combs are particularly attractive for their GHz repetition rates, broad tunability, and intrinsic mutual coherence [28,29]. An EO frequency comb is generated by modulating a continuous-wave laser signal through one or multiple phase and amplitude EO modulators. This modulation process translates the input laser’s single frequency into a comb of equally spaced frequency lines. Traditionally, this is often achieved using off-the-shelf modulators based on lithium niobate (LiNbO3, LN), a material well known for its excellent optical properties and significant χ(2) nonlinearity [30,31]. In recent years, the rapidly emerging thin-film LN (TFLN) platform, with tightly confined optical waveguides and substantially enhanced EO modulation efficiency [32–37], has further enabled integrated EO combs with much higher integration levels and wider comb spans compared with their bulk counterparts [38–40]. In particular, resonant EO combs that leverage optical resonators with ultrahigh quality (Q) factors have achieved remarkable comb spans, since the optical pump can be circulated and modulated for dozens of round trips. For example, an over 80 nm wide EO comb has been achieved in a TFLN optical resonator with a Q factor of 1.5×106 [24]. Further adopting a dual-resonator design has pushed the optical conversion efficiency to 30% with an even wider comb span of 132 nm in wavelength [41].

To date, however, most on-chip resonant EO comb generators make use of a ground-signal-ground (GSG) capacitive electrode for applying the EO modulation signals [Fig. 1(a)]. This electrode configuration is essentially a lumped-capacitor load from the driving circuit perspective, where the input electrical power is almost fully reflected and not efficiently utilized. As a result, several watts of electrical driving power are often required for broadband EO comb generation (e.g., 2.2 W in Ref. [41] and 1 W in Ref. [42]). Moreover, the high reflected electrical power could be detrimental to the driving RF circuit, necessitating bulky and costly isolators or circulators to prevent power reflection to the electrical amplifier [Fig. 1(a)]. In short, the lumped-capacitor electrode design has become a major hurdle in terms of complexity, cost, and power consumption to the practical application of integrated resonant EO combs.

To address these issues, we propose and demonstrate an on-chip coplanar waveguide (CPW) microwave resonator electrode for efficient and RF circuit friendly driving of EO frequency combs. Compared with a conventional lumped-capacitor electrode, our device features a 3.6 times electrical field enhancement, which leads to more than three times reduction in power consumption with negligible electrical power reflection (−46dB). Leveraging a 4-inch wafer-scale TFLN platform, we experimentally demonstrate broadband power-efficient EO frequency comb generation with a repetition rate of 25.6 GHz and a comb span exceeding 85 nm. Importantly, this is achieved using an optical racetrack resonator with a moderate QL=8.5×105, at a relatively low electrical driving power of 28.7 dBm, and without the use of electrical isolators or circulators. The design and analytical model can be readily extended to other RF frequencies, supporting power-efficient EO comb generation with a wide range of target repetition rates.

Figure 1(c) illustrates the working principle of the proposed EO comb generator, consisting of an optical racetrack resonator fabricated in TFLN, integrated with CPW resonator electrodes. High-speed modulating electrical signal is applied to the input GSG microelectrodes, which is capacitively coupled into the CPW resonator by an interdigitated electrode (IDE). The CPW resonator consists of a GSG transmission line with a length equal to a quarter wavelength (λ/4) and shorted terminals on the opposite end, forming a quarter-wave resonator. When the applied microwave signal is near resonance frequency, the electrical field is significantly enhanced at the coupling (open) port, while the shorted end exhibits zero voltage (but finite current flow), following a sinusoidal λ/4 standing-wave pattern along the transmission line [Fig. 1(c)]. Through precise engineering of the IDE to achieve impedance matching between the microwave resonator and the driving circuit, the input electrical power can be critically coupled into the resonator, leading to enhanced EO modulation efficiency and negligible reflected electrical power.

A crucial requirement to achieve efficient EO comb generation is phase matching between the resonant optical- and micro-waves. In our device architecture, this is naturally satisfied when the microwave resonance frequency fMR, the applied microwave frequency fMW, and the optical free-spectral range (FSR) are equal. As the schematic shows in Fig. 1(c), considering a counter-clockwise-traveling optical pulse (green) present at the top middle section of the microwave resonator at time t0, it experiences a positive maximum EO modulation effect if the microwave field is pointing upwards (from signal to ground) at this point. The optical pulse circulates and reaches the bottom middle section of the resonator at time t0+τ/2, where τ=1/FSR is the round-trip time of the optical resonator. Although the electric field at this location is opposite to that in the upper gap [pointing downwards at time t0, as shown in Fig. 1(c)], it exactly flips to the upward-pointing direction at t0+τ/2, as long as the microwave modulation frequency fMW is equal to the optical FSR (such that microwave period TMW=1/fMW=τ). As a result, the optical pulse again sees a positive maximum EO modulation field at t0+τ/2. At other locations of the resonator, although the electric field strength may be smaller, the optical signal always experiences upward-pointing electric field and therefore a constructive accumulation of EO modulation throughout the resonator.

In our device targeting a repetition rate of ∼25GHz, the microwave transmission line has an effective index (neff,MW) of ∼2.6 and an effective wavelength of 4.4 mm, leading to a total length of 1.1 mm for the λ/4 resonator. Meanwhile, the optical group index (ng,O) is 2.26 in the TFLN waveguide at telecommunication wavelengths, necessitating a round-trip length of 5.1 mm for the racetrack resonator. We use a bending radius of approximately 80 μm with a Euler curve shape to minimize bending loss, such that the straight section of the racetrack is 2.3 mm long. This allows the λ/4 resonator to be placed within the left half of the optical resonator to satisfy the phase-matching condition discussed above.

We design and finely tune the microwave resonator and coupling IDE to achieve impedance matching with the external driving circuit at the target resonance frequency. Figure 2(a) illustrates the top-view and cross-section schematic of the CPW microwave resonator. This short-circuit λ/4 resonator can be equivalently modeled by a parallel RLC resonant circuit near resonance [Fig. 2(b)], where the input signal is applied from the driving circuit (ii) into the resonator circuit (i). Assuming there is no extra loss on the transmission line, the total input impedance of (i) is given by Zin=1iωCκ+Rp+ZLCR=1iωCκ+Rp+(1iωL+iωC+1R)−1,(1)where Cκ represents the capacitance of the IDE, Rp is the parasitic resistance of the IDE, and R, L, and C are the equivalent resistance, inductance, and capacitance of the RLC resonator, respectively. Using conformal mapping techniques, the geometric contribution to capacitance Cl and inductance Ll per unit length of a CPW line can be expressed as [43,44] Cl=4ε0εeffK(k0)K(k0′),(2)Ll=μ04K(k0′)K(k0),(3)where ε0 and μ0 are the vacuum permittivity and permeability, respectively. εeff is the effective dielectric constant of the CPW mode spanning across air, LN, and top/bottom cladding, which is estimated to be 5.9 in our device. K(k0) and K(k0′) denote the complete elliptic integrals of the first kind, with the arguments k0=WW+2Sandk0′=(1−k02),(4)where W=155μm is the signal width of the CPW line, and S=7μm is the electrode gap. For nonmagnetic substrates and neglecting kinetic inductance, Ll is determined by the CPW geometry only, whereas Cl depends on both the geometry and εeff. The calculated values are Cl=1.15×10−10F/m and Ll=2.1×10−10H/m in our CPW line. The characteristic impedance is then given by Z0=Ll/Cl,(5)which results in a value of 42.8Ω for the current design. The corresponding total C and L values can then be calculated by multiplying with the length of the CPW line, Ls=1100μm: C=Ls×ClandL=Ls×Ll,(6)and the resistance R can be calculated using the characteristic impedance Z0: R=Z0αLs,(7)where α is the loss coefficient of the transmission line. We obtain α=0.11mm−1 by measuring a long CPW line with the same cross-section configuration, leading to an estimated R=350Ω.

In our design, we intentionally set the characteristic impedance Z0 of the isolated CPW resonator to be below RL=50Ω, since the total input impedance also includes the coupling capacitance Cκ and the parasitic resistance Rp of the IDE following Eq. (1), where the coupling capacitance Cκ can be obtained by Cκ=Cunitcell×Lf×(n−1).(8)

Here Lf is the IDE finger length, n is the number of finger pairs, Cunitcell is the capacitance of each unit cell and can be calculated by Cunitcell=4εeK(k1)K(k1′)andk1=wfwf+2sf,(9)where εe is the relative dielectric constant, wf=3μm is the finger width, and sf =2μm is the finger slot width in our design.

It should be noted that the existence of the coupling capacitor not only changes the input impedance Zin, but also shifts the resonance frequency fMR from the isolated RLC resonance. As a result, deviation in the coupling capacitance Cκ from the design value would cause undesirable impedance and frequency mismatch. In our experimental validation stage, we vary the IDE length Lf to achieve a near 50Ω input impedance at the target frequency to match that of the external driving circuit and minimize power reflection.

We experimentally verify the performance of the designed λ/4 resonator by measuring the reflection coefficient S11=|(Zin−RL)/(Zin+RL)|, which should ideally be zero at 25 GHz, using a vector network analyzer. Figure 2(c) displays the measured responses from a CPW resonator with an optimal finger length Lf=33.5μm (blue), in comparison with that of a lumped-capacitor electrode (red). The fabricated resonator shows a strong resonance dip at 25.67 GHz, with an on-resonance reflection down to −49.8dB. The measured results are also consistent with the calculation results from the equivalent circuit model (yellow), where the slight discrepancy may result from deviations in the geometric dimensions and dielectric constants between theory and actually fabricated devices. Importantly, the power reflection could remain <−20dB (less than 1%) within a relatively broad frequency range of 1 GHz, which provides crucial tolerance and flexibility in practical applications where the optical FSR may not be perfectly aligned with the microwave resonance. In our actual device to be discussed in more details next, the EO comb operates at a repetition rate of 25.612 GHz (dashed line), where the power reflection is −46dB. This is in sharp contrast to the lumped-capacitor case (red) with a −3dB power reflection into the driving circuit (rest is lost in the on-chip resistance).

All devices are fabricated on x-cut TFLN wafers (NANOLN). The wafer stack consists of a 500 nm TFLN layer, a 4.7 μm thermal oxide buffer layer, and a 500 μm high-resistance silicon substrate layer. The TFLN wafer is first coated by a layer of 700 nm thick SiO2 using plasma-enhanced chemical vapor deposition (PECVD) as etch mask. The optical waveguides and optical racetrack cavities are then patterned by an ASML UV stepper lithography system (NFF, HKUST). The patterns are transferred into the oxide mask layer and LN layer sequentially using reactive ion etching (RIE) with a 250 nm etch depth. After removing the remaining etch mask, another layer of PECVD oxide is coated to form a 1.5 μm thick upper cladding of the optical waveguides. The metallic electrodes (750 nm of copper, 50 nm of gold) are formed by a second stepper lithography process, followed by thermal deposition and lift-off. 5 μm wide metallic bridges (800 nm of copper) are then patterned at the short end of the CPW resonator by electron-beam lithography (EBL), thermal deposition, and lift-off processes. Finally, facets of the fabricated devices are cleaved for optical measurements. The fabricated optical bus (racetrack) waveguide has a top width of 1.2 μm (2 μm). Figure 3(a) shows the micrographs of the fabricated EO comb generators with lumped-capacitor (top, as a reference) and CPW resonator electrodes (bottom). Figure 3(b) shows scanning electron microscope (SEM) images with details of the metallic bridges and the IDE.

We experimentally demonstrate power-efficient and RF isolator-free EO comb generation enabled by the CPW microwave resonator. An optical pump from a continuous-wave tunable laser (Santec TSL-550) is launched into the TFLN waveguide via a lensed fiber. The optical output is collected by another lensed fiber and recorded by an optical spectrum analyzer (Yokogawa AQ6370D). The driving microwave signal near 25 GHz is generated by an RF synthesizer and amplified by an electrical power amplifier. For the microwave resonator devices, the amplified electrical signal is applied directly onto the microelectrodes using a GSG probe, without the need of a circulator or isolator, thanks to the excellent impedance matching and minimal power reflection. As for the reference device with lumped-capacitor electrodes, the amplified electrical signal is first passed through a microwave circulator before being delivered to the microelectrodes. The reflected electrical power is then terminated at a 50 Ω load through the circulator, similar to that used in Refs. [24,41]. To compensate for the loss from the circulator (0.9 dB at 25 GHz), the output power from an electrical amplifier is slightly higher than that used for measuring the CPW devices. During the experiments, the optical input pump power is fixed at 2 mW and the applied electrical driving powers on chip are calibrated to be 740 mW (28.7 dBm) in both cases.

Experimental results show that our CPW resonator enables frequency comb generation with an approximately doubled comb span from the reference lump-capacitor device. When the input optical and microwave frequencies are both tuned into resonance with the on-chip optical and microwave resonators, we achieve a broadband EO comb with an 85 nm span and 430 comb lines at a repetition rate of 25.612 GHz [Fig. 3(c) (ii)]. The measured spectral span and roll-off slope (∼0.9dB/nm) are both on par with that reported in Ref. [24] using a similar input RF power, but achieved with an optical resonator with 1.8 times lower loaded QL factor. Since the resonant EO comb span is proportionate to both optical QL and modulation index [45], this indicates an approximately 1.8 times increased electrical power efficiency. To better compare our results with earlier reports, we define a power efficiency figure of merit (FoM) based on the comb span normalized by square root of microwave power and loaded Q factor, as shown in Table 1. It can be seen that our electrical power utilization is significantly higher than that of all previously reported resonant EO comb generators.Table 1.

Comparison of EO Frequency Comb Generators^a

The enhancement in modulation efficiency is further corroborated by comparing the measured EO comb with that of the reference device fabricated on the same chip, which features a comb span of 38 nm (narrower by a factor of 2.2) with a repetition rate of 25.255 GHz [Fig. 3(c) (i)]. Taking into account the slightly lower QL of 6.8×105 in the reference device, the effective modulation enhancement factor of our microwave resonator design is 1.8, which corresponds to more than three times reduction in electrical power consumption. Considering that the signal length (Ls) of the microwave resonator electrode is approximately half (1100 μm) of that in the lumped-capacitor device (2300 μm), we estimate that the average electric field strength in the EO modulation region is enhanced by a factor of 3.6 in the microwave resonator. The EO comb span could in principle be further broadened to >150nm with an improved optical QL factor of 1.5×106 and a higher microwave power of 33.4 dBm {Fig. 3(c) (iii), same condition as that in Ref. [41]}. In this case, a more careful engineering of the waveguide dispersion will likely be required. We note though, operating in a moderate-Q-factor regime in this work also offers distinct advantages for practical applications, as the overall pump-to-comb conversion efficiency is higher (∼0.6%, as compared to 0.3% in Ref. [24]) and the system is less prone to optical and microwave detuning.

Theoretically, our EO comb generator exhibits optimal performance when the microwave resonance frequency fMR is perfectly matched with the optical FSR. To investigate the tolerance to potential mismatch between fMR and FSR that may arise from fabrication deviations, we fabricate and measure a series of devices with identical microwave resonator electrodes but varying optical racetrack resonator sizes. The performance of each EO comb generator is evaluated by fixing the optical pump and microwave driving power, while finely tuning microwave frequency to the optical FSR in each device. As shown in Fig. 4, the generated comb span gradually decreases when the optical FSR shifts away from the CPW resonance frequency at 25.67 GHz. The trend of measured comb span (blue dots) agrees well with the calculated relative electric field strength (black curve). Importantly, the measured comb span remains (∼90% the optimal value) within a relatively broad optical FSR range of 25.4–25.7 GHz, providing important robustness and tolerance in practical scenarios.

The design and analytical model of our CPW resonator can be readily extended to other frequencies. To showcase this scalability, we design and fabricate CPW resonator electrodes with a target resonance frequency near 10 GHz. To achieve this, the signal lengths Ls are set to 2990 μm and 3000 μm, whereas the finger length Lf is optimized to 50 μm for impedance match [Fig. 5(a)]. Figures 5(b) and 5(c) show the S11 parameter measured from the fabricated electrodes, where the resonance frequency locates at 9.82 GHz and 9.67 GHz, respectively, proving excellent control over the resonance frequency. The relatively large power reflection may be attributed to undesirable resistance Rp caused by fabrication imperfections, leading to impedance mismatch and additional electrical power loss.

In conclusion, our EO comb source embedded with λ/4 CPW microwave resonator electrodes not only features substantially improved comb generation efficiency, but also strongly suppresses power reflection back to the driving circuit. The reduced RF power consumption and removal of electrical isolators or circulators are highly desired for such EO combs to be applied in practical and commercial scenarios. The design principles and analytical model developed in this work can be readily extended to other microwave frequencies (and in turn comb repetition rates) by scaling the CPW resonator and IDE lengths. Further improving the fabrication process to reduce metal surface roughness and applying micro-structured electrodes could be helpful in reducing microwave losses, thus achieving a higher modulation efficiency [47]. Our research provides a simple and feasible solution for achieving efficient and low-cost integrated EO frequency combs, promising for applications in precision metrology, advanced spectroscopy, and optical communication systems.

Acknowledgment. We acknowledge Nanosystem Fabrication Facility (CWB) of HKUST for the device/system fabrication.